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Maths/ engineering help!

My partner has just started an engineering apprenticeship having left school after college and going straight into work he's been faced with the most complicated maths we've ever seen!
The question he's been given is as follows

An electric motors power consumption, Y, (in Watts) is found to be
Y=0.4x^2-16x +190
Where x is the angular velocity in revolutions per second. Find the optimum speed for best efficiency, and the power at this speed.

We've got our head around differentiation so we can differentiate but literally clueless as to what to do next. Any help would be greatly appreciated!

Thanks!
Hi, is he completing a level 3 course and is this mathematics for engineering technicians? If so, type the course and assignment title into YouTube, more often than not there would be a tutorial showing how to work out a similar problem! :smile:
hope this helps:
0.4(19)^2-16(19) +190 = 30.4
0.4(20)^2-16(20) +190 = 30
0.4(21)^2-16(21) +190 = 30.4

If you differentiate, you get dy/dx=0.8x-16
if you set dy/dx to be 0 you can find a min/max/inflection point.
dy/dx is 0 when x = 20;
take the derivative one more time:
d2y/dx2 = 0.8 which is positive so it is indeed a minimum.
http://emweb.unl.edu/Math/mathweb/calculus/Image393.gif

Essentially, 30 watts at an angular velocity of 20.
Here's the point you want to find:

Spoiler

(edited 6 years ago)
Reply 3
Avatar for Chryze
Chryze
5
I think this is essentially a find the 'maximum of a curve' type of question do differentiate, dy/dx=0, find what x is then plug back in to the original equation
Original post by Hljones17
x


Since a previous poster just edited their post to cover the calculus stuff, I'm going to put that in spoilers in this post.

Spoiler



There is another way of doing this question by looking at y=0.4(x−20)2+30y=0.4(x-20)^2+30, which is the exact same thing as you posted (it's called completing the square). No calculus required for this, just notice that (x−20)2⩾0(x-20)^2 \geqslant 0 for all real xx ( "anything squared is non-negative" ). You might prefer to work with this, I'm not sure.
(edited 6 years ago)
Capture.PNG32.0KB
Reply 5
Avatar for Hljones17
Hljones17
OP
8
Ok, I shouldn't have said we've got our head around differentiation lol.

We worked out how to break down the equation into

Dy/dx=0.8x-16

But we don't understand how to plot the graphs using this information and how to find the value of x

Thank you for all your replys they are really helpful!
Original post by Hljones17
Ok, I shouldn't have said we've got our head around differentiation lol.

We worked out how to break down the equation into

Dy/dx=0.8x-16

But we don't understand how to plot the graphs using this information and how to find the value of x

Thank you for all your replys they are really helpful!

just set 0.8x-16 to equal 0
0.8x-16=0
then 0.8x=16
x=16/0.8
x=20
It's a daft question, as you're only given the input power, so cannot calculate the efficiency. You can get the minimum power consumed - it's a quadratic with a positive coefficient of the squared term, so the minimum can be calculated easily by completing the square.
(edited 6 years ago)

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